PerFlow: Physics-Embedded Rectified Flow for Sparse Reconstruction
A new generative model called PerFlow (Physics-embedded rectified Flow) has been proposed for reconstructing PDE-governed spatiotemporal fields from sparse and irregular measurements. The method decouples observation conditioning from physics enforcement, using guidance-free conditioning via rectified-flow dynamics and a constraint-preserving projection for hard physics embedding. This addresses the ill-posed nature of reconstruction and improves efficiency and stability over existing generative approaches that require sampling-time gradient guidance. PerFlow also enables uncertainty quantification. The work is published on arXiv (2605.03548).
Key facts
- PerFlow is a physics-embedded rectified flow model.
- It reconstructs spatiotemporal dynamics from sparse measurements.
- The method decouples observation conditioning from physics enforcement.
- It uses guidance-free conditioning and constraint-preserving projection.
- It improves efficiency and stability over gradient-guidance methods.
- It enables uncertainty quantification.
- The paper is on arXiv with ID 2605.03548.
- The approach targets PDE-governed fields.
Entities
Institutions
- arXiv